Question

MATH 123 HW 9 Exponential Modeling Name Due Section work in order to receive full credit. Your friend sends out a chain letter e-mail to 12 people by the next day 15 people have received the letter. Assuming an exponential growth pattern, what is the growth factor for the number chain letters received? Do not round 1. 2. Consider the data in the table. Round all answers to 2 decimal places Time ValueAbsolute Change Relative Change 13.60 14.85 16.10 17.35 18.60 19.85 a. Complete the table by computing the absolute and relative change. b. Which model would better represent this data, linear or exponential? Write a meaningful sentence to explain your answer c. Find the model for this data d. What value does your model predict when time is 8? Do not round. 3. Consider the data in the table. Do not round. Time Value Absolute Change Relative Change 13.60 17.00 21.25 26.56 33.20 41.50 Complete the table by computing the absolute and relative change. Which model would better represent this data, linear or exponential? Write a meaningful sentence to explain your answer Find the model for this data. a. b. c. d. What vaue does your model predict when time is 8? Round to one decimal. Section 9 MATH 123 HW 9 Exponential Modeling 4 According to the 2010 United States Census, the Due population of Lafayette rom 56,397 in 2000. (Note: This increase was over a ten year period or a Construct an exponential model for Lafayette's population. Hint: time is a. b. Use your model to predict Lafayette's population in 2020 (which is 20 years or 2 the start of the model) if the percent increase stays the same. 5. Frogs-A species of frog's population grows 24% every year. Suppose pond. 100 frogs are released into a Construct an exponential model for this population. How many frogs will there be in 5 years How many frogs will there be in 10 years a. b. ? Round to whole number c. ? Round to whole number (Between what 2 years) substance has decayed The half-life of Suppose you have 100 grams of this substance. 6. a radioactive substance is one day, meaning that every day half of the Construct an exponential model for the amount of the substance remaining on a given day a. How much of the substance would be left after a week? Round to 2 decimals b. 7, A certain vehicle loses 35% of its value each year a. If the vehicle has an initial value of $25,000, a b. Compute the value of the vehicle at the end of the 3 construct a model that represents the value after t years. year. Round to nearest dollar every kilometer you climb. The pressure at sea level is about Atmospheric pressure decreases by about 12% for t- number of kilometers above sea level.) Round to 1 decimal place on 8b-d. 8. Construct a model to repr resent the atmospheric pressure at a given altitude in kilometers. a pheres of pressure will you feel at 5.895 kilometers? (Top of Mt. Kilimanjaro of pressure will you feel at 8.848 kilometers? (Top of Mt. Everest) c. How many atmospheres of pressure will you feel at 0.383 kilometers? (highest point in Indiana) of d. How many s HW 9 Exponential Modeling r,123m sts so in an account earning 4% interest that compounds annually if he makes no additional Due or withdrawals, how much will be in the account: (Round to nearest cent.) After 10 years? a. b. After 15 years? c. After 25 years? 10, Lori buys a $1500 certificate of deposit (CD) that earns 6% interest that compounds monthly. How much will the CD be worth in: (Round to nearest cent.) a. 15 years? b. 5 years? 11. Lori gets an offer from another bank that is also paying 6% on CD's, but is compounding interest daily. How much will the $1500 CD be worth in: (Round to nearest cent.) a. 18 months? b. 5 years? 12. Callie has $9000 to invest and needs to decide between two investments: A certificate of deposit paying 3% APR compounded quarterly for 8 years A savings account paying 2.88% APR compounded weekly for 8 years * Which investment should Callie choose? Why? Quantify your answer. 13. If two CD's have the same interest rate and the same principal is invested in each for the same number of years, but one is compounded annually and the other is compounded daily, which one would a wise investor choose? Explain in a meaningful sentence Section 9 MATH 123 HW 9 Exponential Modeling Due Compound Interest $1,600.00 $1,400.00 $1,200.00 $1,000.00 $800.00 $600.00 $400.00 200.00 10 15 Weeks 20 25 30 14. Using the graph above answer the following questions. a. b. c. What is the initial value? Is this exponential growth or decay? Choose the equation that best fits this model. i. y 200( 0.08) ii. y 200 (1.08) iii. У 200x +15 iv, y=5x + 200 Amoxicillin 600

Answer 1

Kindly note that as given in question
12 people were send an email by a friend
By Next day :
15 people received the letter and the number rises exponentially
Let us assume that the number of people receiving the letter is given by At
At	=	A0 * e^ kT
A0	=	12	(Number of people initially sent letter)
k	=	Exponential growth rate
T	=	Time period in number of days
Also when T = 1 day
At	=	15
=>
15	=	12*e^k
1.25	=	e^k
Taking natural logarithm both sides
ln(1.25)	=	ln (e^k)
0.223144	=	k
k	=	0.223144
Hence the growth factor for number of letter received is
	=	0.223144
Solution
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